Contrast agents are commonly used in diagnostic applications, such as for the assessment of blood perfusion in contrast-enhanced ultrasound imaging applications. For this purpose, during an analysis process of a specific body-part of a patient, an ultrasound contrast agent (UCA)—for example, consisting of a suspension of phospholipid-stabilized gas-filled microbubbles—is administered to the patient. The contrast agent acts as an efficient ultrasound reflector, and it can be easily detected by applying ultrasound waves and measuring echo signals that are returned in response thereto. Since the contrast agent flows at the same velocity as red-blood cells in the patient, its detection and tracking in the body-part under analysis provides information about the corresponding blood perfusion.
Particularly, in a quantitative approach, the echo signal is recorded over time during the whole analysis process for each location of the body-part, and it is fitted by a parametric function using a best-fit optimization process. This optimization process generates a time-intensity function, which consists of an instance of the parametric function being defined by the best-fit values of its fitting parameters. The values of different perfusion parameters are calculated from the time-intensity function (such as a time to peak, a mean transit time, and the like); these perfusion parameter values are then used to characterize the corresponding location (for example, for detecting and identifying a lesion). Any perfusion parameter may be calculated from the echo signal over time that is obtained in a predefined Region of Interest (ROI)—with the perfusion parameter value that is then presented as a single value. Alternatively, any perfusion parameter may be calculated from the echo signal over time of each basic portion of the body-part individually; a parametric image is then generated by graphically visualizing the perfusion parameter values of the different basic portions of the body-part (for example in a color-coded representation). The perfusion parameter values provide a quantitative assessment of the blood perfusion in the body-part (with the parametric images representing a spatial map of the perfusion parameter values throughout the body-part).
The contrast agent may be administered to the patient as a bolus (i.e., a single dose provided over a short period of time). The bolus administration is very simple, and it can be carried out by hand (for example, using a syringe); moreover, this requires a small amount of contrast agent. Different examples of quantitative analyses based on bolus administration are disclosed in WO-A-2006/108868, WO-A-2006/067201, WO-A-2009/083557, WO-A-2010/058014, and U.S. Pat. No. 6,216,094, as well as in “Quantification of perfusion of liver tissue and metastases using a multivessel model for replenishment kinetics of ultrasound contrast agents—Martin Krix, Christian Plathow, Fabian Kiessling, Felix Herth, Andreas Karcher, Marco Essig, Harry Schmitteckert, Hans-Ulrich Kauczor, And Stefan Delorme, Ultrasound in Med. & Biol., Vol. 30, No. 10, pp. 1355-1363”, and “A new method of analyzing indicator dilution curves, Cardiovascular Research—R. A. F. Linton, N. W. F. Linton and D. M. Band, vol. 30, pp. 930-938, 1995 (the entire disclosures of which are herein incorporated by reference).
Particularly, WO-A-2009/083557 discloses a method for detecting and quantifying targeted contrast agent that immobilizes on a specific target. For this purpose, the echo signal is fitted by an instance of a model function based on a combination of a circulation function (modeling the circulation of the contrast agent) and a dynamic immobilization function (modeling the immobilization of the contrast agent and the decay of its echo signal). In a specific implementation, the fitting operation is performed in two optimization steps. At first, an initial portion of the echo signal is defined up to a predefined multiple of its peak instant (when the echo signal reaches the maximum value thereof). The initial portion of the echo signal is fitted by an instance of the same circulation function alone, so as to determine the values of the corresponding fitting parameters (i.e., A, m and s in the case of a lognormal distribution function). This instance of the circulation function provides a good estimate of each signal (since only a small fraction of the contrast agent immobilizes at the beginning); moreover, the dynamic immobilization function depends on the circulating function (i.e., on its integral). Therefore, the same fitting parameters A, m and s of the model function may be initialized substantially exactly to the values determined above (and constrained to vary during the corresponding optimization step within a predefined range thereof); the fitting of the echo signal by the model function may then be focused on the determination of its remaining fitting parameters alone (i.e., an immobilization parameter and a decay parameter).
Typically, the parametric function consists of a simple bolus function (for example, the lognormal distribution function), as used in classical indicator-dilution approaches, which is adapted to model the typical trend of the echo signal over time (with a wash-in followed by a wash-out of the contrast agent). However, the simple bolus function is generally unable to model a second passage of the contrast agent following a first passage thereof (for example, due to its re-circulation through the body-part, following the normal cycle of circulation of the blood in the patient). Particularly, when the second passage of the contrast agent reaches the body-part before completion of the first passage, the resulting time-intensity function is not very accurate in describing the actual trend of the echo signal over time and therefore it is unable to accurately describe the perfusion of the body-part by the contrast agent—with corresponding errors in the resulting perfusion parameter values, which adversely affect a quality of the analysis process.
In order to tackle this problem, several methods for separating the first passage from the second passage of the contrast agent have been proposed in the art—for example, as described in the above-mentioned documents U.S. Pat. No. 6,216,094 and “R. A. F. Linton, N. W. F. Linton and D. M. Band”. However, these methods become unreliable when there is a substantial degree of encroachment of the second passage on the first passage and/or when the second passage starts before a peak instant of the first passage.
Alternatively, the above-mentioned document WO-A-2006/067201 proposes the use of a combined bolus function that consists of the sum of a first simple bolus function (for the first passage of the contrast agent) and a second simple bolus function (for the second passage of the contrast agent). The combined bolus function allows obtaining an accurate representation of the first passage of the contrast agent, which contains the most relevant information about the perfusion of the corresponding location of the body-part (with the perfusion parameter values being calculated from the first time-intensity function facilitating its characterization).
However, the combined bolus function now includes a high number of fitting parameters (i.e., twice the ones of the simple bolus function). Therefore, the fitting of the echo signals by the combined bolus function (for determining the corresponding time-intensity functions) is quite problematic. Particularly, this may cause instabilities in the applied algorithm (for example, because of ambiguities or convergence errors), and/or it may result in unreliable estimates of the fitting parameters (and then of the corresponding perfusion parameters); the problem is especially important when the fitting is applied on noisy echo signals.